Triangle dissection problems

Let ABC be a triangle and let D be a point between B and C. Then we say that ABC has been dissected into the two triangles ABD and ACD.

1. Show every triangle can be dissected into two right triangles.

2. What can you say about a triangle which can be dissected into two isosceles right triangles?

3. A right triangle with short leg 1 unit in length can be dissected into an isosceles right triangle and another isosceles triangle (not right, however). How long is the hypotenuse of the original triangle?

4. A certain triangle can be dissected into two triangles, one of which is equilateral with side 1 and the other of which is isosceles. Find all sides and angles of the original triangle.

5. Can a 30-60 degree right triangle be dissected into two isosceles triangles?

6. Find all isosceles triangles (not right) which can be dissected into two isosceles triangles.

7. Find all triangles which can be dissected into two triangles each of which is similar to the original triangle.

8. Make up a triangle dissection problem.